A base-motif fractal is a type of fractal which is created by an iterated process in which a certain element of the base is replaced by the motif and this becomes the new base. For example, the Koch snowflake can be constructed as a base-motif fractal in which the objects being replaced are lines.

The number of sides grows exponentially as this process continues, but, at least for this fractal, the edges never run into each other.